{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we go through clustering methods over correlation distance matrix,\n",
    "$d_{i, j} = \\sqrt{\\frac{1}{2} (1 - \\rho_{i, j})}$. Especially, we try out k-means clustering. In k-means algorithm, you need to pick up the number of clusters, K, in advance. To tune this parameter, we introduce clustering quality metric, silhouette coefficient,\n",
    "$$S_i = \\frac{b_i - a_i}{max\\{a_i, b_i\\}}, \\forall i = 1, ..., N$$\n",
    ", where $b_i$ and $a_i$ are average distance from different cluster points and the same cluster points.\n",
    "\n",
    "If clustering is completely at random, these two distance would be closer, so $S_i$ would be around zero on the average. The better quality, the close to 1 the metric becomes. To aggregate value on each point, we use the following\n",
    "$$q = \\frac{Mean[S_i]}{Std[S_i]}$$\n",
    "\n",
    "Our clustering algorithm is briefly the following:\n",
    "1. Find the best kmeans over 1-K cluster numbers\n",
    "2. Iterate with different initialization\n",
    "3. Try further 1 and 2 on set of clusters: $\\{q_k | q_k < E[q],  k=1, ..., K\\}$\n",
    "\n",
    "Step 1 and 2 are implemented as `cluster_kmeans_base`. Step 1-3 are implemented as `cluster_kmeans_top`. \n",
    "\n",
    "The detail of implementations will be found at finance_ml/clustering.py."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiments on Random block Correlation Matrices\n",
    "\n",
    "We generate correlation matrix, where strong correlation only within the same block."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 100)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tom/anaconda3/lib/python3.8/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.neighbors.kde module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.neighbors. Anything that cannot be imported from sklearn.neighbors is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    },
    {
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       "<p>5 rows × 100 columns</p>\n",
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      "text/plain": [
       "         0         1         2         3         4         5         6   \\\n",
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       "2  0.598048  0.601135  1.000000  0.610707  0.597224  0.615816  0.611040   \n",
       "3  0.600005  0.624170  0.610707  1.000000  0.602963  0.615655  0.612424   \n",
       "4  0.586387  0.585657  0.597224  0.602963  1.000000  0.622056  0.598502   \n",
       "\n",
       "         7         8         9   ...        90        91        92        93  \\\n",
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       "1  0.609609  0.617839  0.616108  ...  0.310329  0.311193  0.302927  0.301981   \n",
       "2  0.614288  0.607739  0.614309  ...  0.309978  0.309934  0.298900  0.299113   \n",
       "3  0.597758  0.617270  0.610358  ...  0.300279  0.308027  0.300878  0.304078   \n",
       "4  0.606087  0.608740  0.608062  ...  0.308816  0.319117  0.312151  0.296105   \n",
       "\n",
       "         94        95        96        97        98        99  \n",
       "0  0.322649  0.304136  0.320738  0.315558  0.305778  0.313103  \n",
       "1  0.310100  0.292801  0.308539  0.299938  0.292367  0.307086  \n",
       "2  0.302103  0.298401  0.302921  0.298104  0.297159  0.304467  \n",
       "3  0.309388  0.294256  0.303846  0.298484  0.288817  0.309580  \n",
       "4  0.314826  0.298759  0.317565  0.307786  0.302360  0.311999  \n",
       "\n",
       "[5 rows x 100 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from finance_ml.experiments import get_random_block_corr\n",
    "\n",
    "x = get_random_block_corr(100, 10, is_shuffle=False, sigma=1)\n",
    "print(x.shape)\n",
    "x.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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n0xfVspL0RLW8JD3RUV7Snoh7LOL2RbW8JH3RUV6Svqi2Lk7SG3HX2XF7w2fdHqc34uTF7Y2oLN/eiMrz7Y1qeUl6w+dYxOmNqDzf3qiW59sb1a7xkvRF3GvGuH3hcw0a1Rdxsnzmi6g8376IyvPti2p5SfrC51jE6YuoPJ++qJaVZL6Iulfh2xs+9z7i9IbvvZSo3oibF7c/4uTF7Y84WT69EZXn2xu+xyKqN+Lk+fRGVF4t1+Cb33er9b5Utft4vtffUfcEfe9LdZSX9L5Ue3m13JdqL6+W+1Kb59V6XyrqePhcf7eXVct9qc3zkvRE1P1j397wuR8dpzd8729X64+4WXF7I06eT2/EyfPpjag8397wPRZRvREnz6c/ovJ8+6Pa6yBJ5oy4r6vEnTN8XqeJM2/EyfOZN6LyfHojKst3zqiWl2TO8DkWceaMqDzfeaNaXq2vZwD429hqNsM8++yzbb5/2WWXud13373mfMvNMD/4wQ/c4MGD3f/8z//UlFMsFt2yZcvcSy+95C666CLXt29f99Zbb3nnrFixwvXr18+9+uqrm75Xy2aYza1bt87179/f/cu//Euiv8/n827UqFFtvvfDH/7QffWrX625trFjx7pjjz22pox7773X7bLLLu7ee+91r7/+urvrrrvcDjvs4O64447Eme+884477LDDnCSXzWbdgQce6CZOnOiGDRvmldPRZpiVK1e2+b3TTz/dHXXUUd55n2e5Gaa1tdWNHz/e7bfffm7NmjU15a1bt84tW7bMPffcc+573/ue23XXXTv83MlqeYsXL3b9+/dvs/iudTPM5lauXOny+bz7j//4D++8jWPgd77znTa/d9xxx7kTTzyx5vp23313d84550TmdJQ1Z84ct9tuu7mHH37Yvfbaa+6GG25wPXv2dAsWLEiUt3jxYjd8+PBNPXLUUUe5cePGuXHjxkXmtTcGJ+2NqPHcty+i8nx7o1pekt5oL6+W3og7H8btjfbykvZGnNp8+qKjvKS90VGeb290tJZI2hNx1iY+fREnz6cvovJ8+qKjrKQ94bOui9MTHeUl7Ym49cXti2p5SfqiWp5PX0Sti317w2edHac3fPLi9EbcvDi9EZXl2xtJrlGq9UZUnm9v+NYX1Rtx8nx6I05eLeupz1/j1XqNsXne5yX9aL2O8pJcZ7SXlfQaY/O8Wq8xOqrv83yuMTbPq/UaI6o+n7VUR3m1XGdsnuXbE1H3Knx7w+feR5ze8MmL0xtx8+L2R1SeT38kuW9UrTei8nx7w7e+qN6Ik+fTG3Hyks4Zm993q3XOqHYfz3fOqJaVZL7oKC/pnLF5Xq1zRpx7oD5zxuZ5tc4ZUfX5zBntZdUyX7SX59sTUfePfXvD5350nN7wyYvqj7hZcXsjKs+3N5Lcy6/WG1F5vr3hW19Ub8TJ8+mPOHk+/VHtdZAkc0bc11Xizhlx8+LOG3HyfOaNanm+veH7mlTUnFEtL8mc4VNfnDkjKs933ojKq+X6G8DfRuo3wxSLRZfNZt0DDzzQ5vs/+tGP3GGHHVZzvtVmmHPOOcftsssubvny5TVnbe7rX/+6+/73v+/9dw8++OCmAXjjlyQXBIHLZrOuXC7XXNsRRxzhzjrrrER/O2jQIHfaaae1+d7cuXPdzjvvXFNNf/rTn1wmk3EPPfRQTTm77LKLu/HGG9t8b/bs2SabsNatW7dpsXfCCSe4Y445xuvvNz9v3333XSfJvfzyy21+75vf/KY75ZRTvPM+z2ozTGtrq5swYYLbd999vd5NKG6P/t3f/V2sd+7ZPO+nP/3ppp74fJ9kMhk3ePBg0/o+/zmocfOKxaLL5XJu9uzZbX5v6tSp7h/+4R9qqu/pp592ktq8mOKTtX79epfP57f4zMzTTjut5k1Yf/nLX9yHH37onHPuoIMOcj/4wQ+qZnU0BifpjTjjuU9fROX59obvfBPVGx3lJe2NJPVV642O8pL0RpzafPqio7ykvRGnPt/e2GjjWqLW+WLzvM9L+sJme3lJ54xq9X1e3Dnj81m1zhc+tcWZLzbPq3W+qFaf73zRXl6tc0a1+uL0RdS6+J133vHqDZ91dpzeiJsXtzeSXge01xtRWddcc41Xb9RSW3u9EZXX0tLi1Rs+9cXpjai8devWefWGT31J54yN13hWc0Z714y1zBmb59UyZ0Rdz/rMF5/Ps5oz4tTnM2dszLOaM9qrr5Y5Y2OexZzRXm1xeyLqXoVvb/jc+4jTG3Hz4vZG0nszHfVHVJ5Pf9RSW3u9EZXn2xs+9cXpjag8397wqc9nzmjvvlstc0bUfTyfOaNaVpL5wuceY5w5o728WuYM3/qi5oz28mqZM6Lq85kz2suqZb6Iqi1uT0TdP/btDZ/70XF6I25enP5Ieq+8o96IyvPtjVrqa683ovJ8e8Onvji9EZXn2x8+9fnMGe29DlLLnBH1uorvdUa1vCTzhs/rPnHmjfbyks4bvrVFzRnt5dUyZ0TV53ud0V5eLfNGVH1Jr78BdL6MUq6urk4jR47UggUL2nx/wYIF+od/+Icuqup/Oed0zjnn6IEHHtBvf/tbDRkypFP+Gxs/e87H17/+db3xxht69dVXN30dcMABmjhxol599VVls9ma6ioWi/rjH/+onXbaKdHfH3zwwVq6dGmb77399tsaPHhwTXXdfvvt6tevn77xjW/UlLN+/XplMm1bJJvNKgzDmnIlqUePHtppp530ySef6De/+Y3Gjx9fU96QIUM0YMCANn3S2tqq3/3ud6nok1KppBNOOEHLli3TE088oR133NH8v5G0T04++WS9/vrrbfpk55131oUXXqjf/OY3JrV99NFH+p//+Z9EvVJXV6cDDzywU3rl5z//uUaOHBnrM63bUyqVVCqVOqVPevfurS9+8YtatmyZFi9e3GGPRI3BPr1hPZ7HyfPpjaT1ddQbUXm+vZGkvmq9EZXn0xs+tcXpi6g8397wqS9ub7T33ygWi2bzRdIxN06exZwRVZ9P/Rt/12q+qPbfTjJfbMyzmi/aq6+W+WJjntWc0V59cfoial08dOhQr96wXmfHyfPpjaT1tff8RmWdeuqpXr2RpLZqvRGVVygUvHrDp744vRGVV6lUvHrDp74kc8bnr/Es5oxarxmj8mqZM+LU5jNffD7PYs6Iqs93zvh8nsWc0VF9SeeMz+fVOmd0VFvcnoi6V+HbG9b3PuLk+fRG0vo66o+oPJ/+SFJbtd6IyvPtDZ/64vRGVJ5vb/jU5zNntHffrZY5w+o+XrWspPOFT21x5oz28mqZM+LWF3fOaC+vljkjqj6fOaO9rFrmi6ja4vZE1P1j396wvh8dJy9ufyStraPeiMrz7Y0k9VXrjag8397wqS9Ob0Tl+faHT30+c0Z7r4PUMmdYv67SUV7SecOnvjjzRnt5SeeNuLXFnTPay6tlzoiqz/c6o728WuaNqPqS3rMF8DfwN9hwU7N58+a5fD7vfv7zn7slS5a4yZMnux49erg//elPifI+/fRT98orr7hXXnnFSdr02XXvvfeed9b/+T//x/Xu3ds99dRTrrm5edPX+vXrE9U2ffp09/TTT7umpib3+uuvu4svvthlMhn3+OOPJ8rbXC0fk3TBBRe4p556yi1fvtw9//zz7thjj3Xbb7994uPw4osvulwu5y6//HK3bNkyd88997jtttvO3X333YnynHOuUqm4QYMGuWnTpiXO2GjSpElu4MCB7tFHH3VNTU3ugQcecH379nVTp05NnDl//nz3X//1X2758uXu8ccfd8OHD3cHHXSQa21tjfzbqPP2yiuvdL1793YPPPCAe+ONN9x3vvMdt9NOO7m1a9cmyvvoo4/cK6+84h577DEnyc2bN8+98sorrrm52SurVCq5b37zm26XXXZxr776aps+KRaL3rWtW7fOTZ8+3T333HPuT3/6k/vDH/7gTjvtNFcoFNybb76Z6LFuLurtaKvlffrpp+6CCy5wzz77rGtqanILFy50o0aNcgMHDkx8LB544AGXz+fdrbfe6pYtW+ZuuOEGl81m3TPPPJP48a5Zs8Ztt9127qabburwccbJGj16tNtrr73cwoUL3fLly93tt9/u6uvr3dy5cxPl/fKXv3QLFy507777rnvooYfc4MGD3fHHH99hfXHG4Li9ESfLpy+i8nx7IyrPtzeSzF/VeiMqz7c34tQXtzfiPta4fREnz6c34uT59EbUWsJ3vojK8+mLqLwkc0a1PN++8F2HRc0X1fKSzBdR9fnOF3Eeb9y+iJPnO2dE5fnOGZvbfF3s2xtReb69US0vSW9Uy0uynqr2WDfn+3Ewn89L0htR9fn2RlSec369EZXn2xtReT69EXWN59sXUXm+fVEtz7cvqmUl6Qnf6+OovqiWl6Qvourz7Ys4j9enL6LyfPoiKst3vohzr8KnN+Lk+fRGVJ5vb0Tl+fZHkns9HfVHVJZvb8Spzac34j7WuL0RJ8+nN+Lk+fZHtftuSdZS1fJ854yOspKuozrKS7qO8rlnGWct1VFe0rVUtfqSrKWiHq/PnFEtK8k6qlqeb0/EuX/s0xtx8nx6IyrPpz+isnx7I8m992q9EZXn2xtx6vPpjbiPN25vxMnz6Y84eT79EfU6iO+cEZXnO2dUy0syb1TLSzJv+L6OVK03qmUlmTOiavOdM+I8Vp85IyrPd96Iyqv13hSAzrdVbIZxzrmf/exnbvDgwa6urs7tv//+7ne/+13irIULFzpJW3xNmjTJO6u9HEnu9ttvT1Tb9773vU2P84tf/KL7+te/brYRxrnaNsN8+9vfdjvttJPL5/Nu5513dscff7x76623aqrnkUcecXvvvbcrFApujz32cLfeemtNeb/5zW+cJLd06dKacpxzbu3ate7cc891gwYNcvX19W7o0KFuxowZsV9waM99993nhg4d6urq6tyAAQPc2Wef7f7yl7/E+tuo8zYMQzdz5kw3YMAAVygU3GGHHebeeOONxHm33357uz+fOXOmV9bGtyZs72vhwoXetW3YsMH94z/+o9t5551dXV2d22mnndw3v/lN9+KLLyZ+rJuLuulQLW/9+vVu7Nix7otf/KLL5/Nu0KBBbtKkSW7FihU11ffzn//c/d3f/Z2rr693w4cPr/oWuHHybrnlFtfQ0BB5/kVlNTc3u1NPPdXtvPPOrr6+3u2+++7uX/7lX1wYhonyrrvuOrfLLrtseu4uueSSqj0XZwyO2xtxsnz6IirPtzei8nx7I8n8Va03ovJ8eyNufXF6I25W3L6Ik+fTG3HyfHojai3hO19E5fn0RVRekjmjWp5vX/iuw6Lmi2p5SeaLOPX5zBdx8uL2RZw83zkjKs93ztjc5uti396IyvPtjWp5SXqjWl6S9VS1x7q5WjbDJOmNOPX59EacPJ/eiMrz7Y2oPJ/eiLrG8+2LqDzfvqiW59sX1bKS9ITv9XFUX1TLS9IXcerz6Ys4eT59EZXn0xdRWUnmi6h7Fb69EZXn2xvV8pLMGdXykvSH772eav1RLStJb8Spzac34uT59EZUnu+cEZXn2x/V7rslWUtVy/Pti46ykq6jOspLuo7yuWcZZy3VUV7StVRUfb5rqag8n76olpVkHVUtz7cn4tw/9umNOHk+vRGV59MfUVm+vZHk3nu13ojK8+2NuPXF7Y24eXF7I06eT3/EyfPpj6jXQXznjKg83zmjWl6SeaNaXpJ5w/d1pGq9US0ryZwRpzafOSNOns+cEZXnO29E5dV6bwpA5wucc04AAAAAAAAAAAAAAABAN5CJ/hUAAAAAAAAAAAAAAABg68BmGAAAAAAAAAAAAAAAAHQbbIYBAAAAAAAAAAAAAABAt8FmGAAAAAAAAAAAAAAAAHQbbIYBAAAAAAAAAAAAAABAt8FmGAAAAAAAAAAAAAAAAHQbbIYBAAAAAAAAAAAAAABAt8FmGAAAAAAAAAAAAAAAAHQbbIYBAAAAAAAAAAAAAABAt8FmGAAAAAAAAAAAAAAAAHQbbIYBAAAAAAAAAAAAAABAt8FmGAAAAAAAAAAAAAAAAHQb/z8SoXJtZFCmNwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 3200x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.heatmap(x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before shuffling, you see several blocks in the correlation matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3200x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from finance_ml.experiments import get_random_block_corr\n",
    "\n",
    "x = get_random_block_corr(100, 10, is_shuffle=True, sigma=1)\n",
    "sns.heatmap(x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's re-find clusters from this matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of clusters: 10\n",
      "{0: [1, 79], 1: [31, 40, 54, 59, 77, 97, 98], 2: [5, 6, 8, 13, 14, 15, 21, 24, 25, 27, 29, 33, 36, 43, 45, 51, 52, 56, 62, 69, 75, 80, 81, 83, 85, 86, 87, 88, 89, 91, 92, 94, 95], 3: [0, 7, 9, 10, 11, 12, 18, 26, 28, 38, 42, 48, 49, 63, 65, 66, 67, 68, 71, 82, 96], 4: [19, 23, 30, 61, 84, 90, 99], 5: [3, 35, 44, 47, 50, 57, 64, 78], 6: [2, 16, 32, 39, 55, 70, 72], 7: [22, 37, 41, 46, 76, 93], 8: [17, 58, 60], 9: [4, 20, 34, 53, 73, 74]}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3200x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from finance_ml.clustering import cluster_kmeans_top, cluster_kmeans_base\n",
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "corr1, clstrs1, silh1 = cluster_kmeans_top(x, 20, n_init=10)\n",
    "print(f\"The number of clusters: {len(clstrs1)}\")\n",
    "print(clstrs1)\n",
    "sns.heatmap(corr1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Successfully reverse correlation back to clustered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stability of the number of clusters\n",
    "\n",
    "Estimating the number of clusters involves stochasticity. So, we estimate its stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2277a61f2bee4ca08108c112541f09c0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=50.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "from tqdm import tqdm_notebook\n",
    "\n",
    "from finance_ml.experiments import get_random_block_corr\n",
    "from finance_ml.clustering import cluster_kmeans_base, cluster_kmeans_top\n",
    "\n",
    "\n",
    "n_iter = 50\n",
    "N = 100\n",
    "KN_ratio = np.linspace(0.1, 0.5, 5)\n",
    "top_data = list()\n",
    "data = list()\n",
    "for i in tqdm_notebook(range(n_iter)):\n",
    "    for ratio in KN_ratio:\n",
    "        ratio = round(ratio, 2)\n",
    "        n_blocks = max(2, int(round(ratio * N)))\n",
    "        max_num_blocks = max(20, n_blocks + 10)\n",
    "        x = get_random_block_corr(N, n_blocks=n_blocks, is_shuffle=False, sigma=1)\n",
    "        corr1, clstrs1, silh1 = cluster_kmeans_top(x, max_num_blocks, n_init=10)\n",
    "        est_n_blocks = len(clstrs1)\n",
    "        top_data.append({\"K/N\": ratio, \"E[K]/K\": est_n_blocks / n_blocks})\n",
    "        corr1, clstrs1, silh1 = cluster_kmeans_base(x, max_num_blocks, n_init=10)\n",
    "        est_n_blocks = len(clstrs1)\n",
    "        data.append({\"K/N\": ratio, \"E[K]/K\": est_n_blocks / n_blocks})\n",
    "data = pd.DataFrame(data)\n",
    "top_data = pd.DataFrame(top_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3200x1600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "tips = sns.load_dataset(\"tips\")\n",
    "sns.boxplot(x=\"K/N\", y=\"E[K]/K\", data=data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3200x1600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "tips = sns.load_dataset(\"tips\")\n",
    "sns.boxplot(x=\"K/N\", y=\"E[K]/K\", data=top_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
